On codes, matroids, and secure multiparty computation from linear secret-sharing schemes

Error-correcting codes and matroids have been widely used in the study of ordinary secret sharing schemes. In this paper, the connections between codes, matroids, and a special class of secret sharing schemes, namely, multiplicative linear secret sharing schemes (LSSSs), are studied. Such schemes are known to enable multiparty computation protocols secure against general (nonthreshold) adversaries.Two open problems related to the complexity of multiplicative LSSSs are considered in this paper. The first one deals with strongly multiplicative LSSSs. As opposed to the case of multiplicative LSSSs, it is not known whether there is an efficient method to transform an LSSS into a strongly multiplicative LSSS for the same access structure with a polynomial increase of the complexity. A property of strongly multiplicative LSSSs that could be useful in solving this problem is proved. Namely, using a suitable generalization of the well-known Berlekamp–Welch decoder, it is shown that all strongly multiplicative LSSSs enable efficient reconstruction of a shared secret in the presence of malicious faults. The second one is to characterize the access structures of ideal multiplicative LSSSs. Specifically, the considered open problem is to determine whether all self-dual vector space access structures are in this situation. By the aforementioned connection, this in fact constitutes an open problem about matroid theory, since it can be restated in terms of representability of identically self-dual matroids by self-dual codes. A new concept is introduced, the flat-partition, that provides a useful classification of identically self-dual matroids. Uniform identically self-dual matroids, which are known to be representable by self-dual codes, form one of the classes. It is proved that this property also holds for the family of matroids that, in a natural way, is the next class in the above classification: the identically self-dual bipartite matroids.

Flow-R, a model for susceptibility mapping of debris flows and other gravitational hazards at a regional scale

The development of susceptibility maps for debris flows is of primary importance due to population pressure in hazardous zones. However, hazard assessment by processbased modelling at a regional scale is difficult due to the complex nature of the phenomenon, the variability of local controlling factors, and the uncertainty in modelling parameters. A regional assessment must consider a simplified approach that is not highly parameter dependant and that can provide zonation with minimum data requirements. A distributed empirical model has thus been developed for regional susceptibility assessments using essentially a digital elevation model (DEM). The model is called Flow-R for Flow path assessment of gravitational hazards at a Regional scale (available free of charge under www.flow-r.org) and has been successfully applied to different case studies in various countries with variable data quality. It provides a substantial basis for a preliminary susceptibility assessment at a regional scale. The model was also found relevant to assess other natural hazards such as rockfall, snow avalanches and floods. The model allows for automatic source area delineation, given user criteria, and for the assessment of the propagation extent based on various spreading algorithms and simple frictional laws.We developed a new spreading algorithm, an improved version of Holmgren's direction algorithm, that is less sensitive to small variations of the DEM and that is avoiding over-channelization, and so produces more realistic extents. The choices of the datasets and the algorithms are open to the user, which makes it compliant for various applications and dataset availability. Amongst the possible datasets, the DEM is the only one that is really needed for both the source area delineation and the propagation assessment; its quality is of major importance for the results accuracy. We consider a 10m DEM resolution as a good compromise between processing time and quality of results. However, valuable results have still been obtained on the basis of lower quality DEMs with 25m resolution.

On fast-decodable space-time block codes

We focus on full-rate, fast-decodable space–time block codes (STBCs) for 2 x 2 and 4 x 2 multiple-input multiple-output (MIMO) transmission. We first derive conditions and design criteria for reduced-complexity maximum-likelihood (ML) decodable 2 x 2 STBCs, and we apply them to two families of codes that were recently discovered. Next, we derive a novel reduced-complexity 4 x 2 STBC, and show that it outperforms all previously known codes with certain constellations.

On high-rate full-diversity 2x2 space-time codes with low-complexity optimum detection

The 2×2 MIMO profiles included in Mobile WiMAX specifications are Alamouti’s space-time code (STC) fortransmit diversity and spatial multiplexing (SM). The former hasfull diversity and the latter has full rate, but neither of them hasboth of these desired features. An alternative 2×2 STC, which is both full rate and full diversity, is the Golden code. It is the best known 2×2 STC, but it has a high decoding complexity. Recently, the attention was turned to the decoder complexity, this issue wasincluded in the STC design criteria, and different STCs wereproposed. In this paper, we first present a full-rate full-diversity2×2 STC design leading to substantially lower complexity ofthe optimum detector compared to the Golden code with only a slight performance loss. We provide the general optimized form of this STC and show that this scheme achieves the diversitymultiplexing frontier for square QAM signal constellations. Then, we present a variant of the proposed STC, which provides a further decrease in the detection complexity with a rate reduction of 25% and show that this provides an interesting trade-off between the Alamouti scheme and SM.

Low-density parity-check codes for nonergodic block-fading channels

We design powerful low-density parity-check (LDPC) codes with iterative decoding for the block-fading channel. We first study the case of maximum-likelihood decoding, and show that the design criterion is rather straightforward. Since optimal constructions for maximum-likelihood decoding do not performwell under iterative decoding, we introduce a new family of full-diversity LDPC codes that exhibit near-outage-limit performance under iterative decoding for all block-lengths. This family competes favorably with multiplexed parallel turbo codes for nonergodic channels.

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